{
  "abstract": "We study the $L^p$-boundedness of Isozaki--Kitada type modified wave operators associated with Schrödinger operators $P=-\\partial_x^2 + V$ in one dimension for potentials $V$ including long-range potentials such as negative Coulomb-like ones $V(x) = -(1+|x|^2)^{-μ/2}$ for $μ>0$. For such potentials, if $ μ\\in (1, 2)$, we prove that the middle and the high energy parts are bounded on $L^p (\\mathbb{R})$ for any $p \\in [1, \\infty]$ but the low energy part is unbounded except for $p=2$. Moreover, if $μ\\in (0, 1]$, we show that even the middle energy part is unbounded except for $p=2$. Actually, regarding the $L^p$-boundedness in the middle and the high energy regimes, we give a complete classification of slowly decaying potentials without imposing any sign condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29729",
  "author_total": 2,
  "authors": [
    {
      "name": "Akitoshi Hoshiya"
    },
    {
      "name": "Kouichi Taira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25fkxpdqx8vt4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29729",
  "fulltext_url": null,
  "id": "25fkxpdqx8vt4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29729",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214324886",
  "pdf_url": "https://arxiv.org/pdf/2609.29729",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25fkxpdqx8vt4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29729",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29729"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Modified wave operators are unbounded on $L^p$ for $p\\neq 2$",
  "title_text": "Modified wave operators are unbounded on L^p for p≠ 2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/25fkxpdqx8vt4",
  "venue": "arXiv",
  "versions": []
}